Geodesic
Best approximations and widths of some classes of convolutions in $L_{2}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 284-294

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We find tight upper bounds for the best approximations by trigonometric polynomials of certain classes of periodic functions representable as convolutions with structural characteristics defined by various modifications of m-th order moduli of continuity in the metric of $L_{2}$. We also find exact values for the $n$-widths of convolution classes given by such smoothness characteristics.
Keywords: best approximation, periodic function, trigonometric polynomial, modulus of continuity of $m$th order, $n$-widths. 
@article{TIMM_2016_22_4_a26,
     author = {K.Tukhliev},
     title = {Best approximations and widths of some classes of convolutions in $L_{2}$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {284--294},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a26/}
}
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K.Tukhliev. Best approximations and widths of some classes of convolutions in $L_{2}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 284-294. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a26/